Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

420. COROLLARIV M.

_H_Inc apparet, ſi producatur, GO, btcunq; in, E, & circa ſemiaxes,
bel ſemidiametros, HO, OE, deſcribi intelligatur ſemicirculus,
vel ſemiellipſis, HEA, quod, ſi etiam producantur, ST, VX, in, N,
M, & iungantur, HN, HM; omnia quadrata trianguli, HXM, ad
omnia quadrata trianguli, HTN, regula, OE, erunt in ratione com-
poſita ex ea, quam habet quadratum, XM, ad quadratum, TN, . i re-
ctangulum, AXH, ad rectangulum, ATH, & ex ea, quam habet,
XH, ad, HT, . i. erunt, bt parallelepipedum ſub altitudine, AX, baſt
quadrato, XH, ad parallelepipedum ſub altitudine, AT, baſi qua-
drato, TH.

421. THEOREMA X. PROPOS. XI.

SI ad axim, vel diametrum datæ parabolæ ordinatim ap-
plicentur duę rectæ lineę eandem ſecantes, deinde ſum-
pto extremo puncto minoris dictarum ordinatim applicata-
rum, & alio extremo puncto maioris dictarum, ſed non ad
eandem partem, iungantur dicta puncta recta linea; hæc di-
uidet quadrilineum duabus ordinatim applicatis incluſum
in duo trilinea: Trilineum igitur conſtitutum in maiori di-
ctarum linearum ad trilineum cõſtitutum in minori tanquam
in baſi erit, vt dicta maior ordinatim ductarum, ſimul cum
tertia proportionali duarum, quarum prima eſt tripla com-
poſitę ex minori, & dimidia exceſſus maioris ſuper minorem,
ſecunda autem eſt dimidia dicti exceſſus, ad eandem mino-
rem, cum eadem tertia proportionali.

Sit ergo parabola, cuius baſis, BH, axis, vel diameter, NO, due
adipſam vtcunque ordinatim applicatæ ſint, BH, baſis, & , AM,
minor ipſa, BH, abſcindens parabolam, ANM, ſumatur autem
vtcunque punctum, A, extremum minoris, AM, & punctum, H,
ad aliam partem de duobus extremis maioris, BH, & iungantur, A,
H, puncta recta linea, AH, deindeà punctis, A, M, demittantur
verſus, BH, parallelæipſi, NO; AC, MG, erit ergo, BC, GH,
exceſſus, BH, ſuper, AM, & , BC, æqualis ipſi, GH, dimidium
dicti exceſſus; fiat etiam, vt tripla, HC, ad, BC, ita, BC, ad, C

Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer